Question

Find the distance between the two points. A(0,1) and B( 6, 3.5)

Answer 1

Answer:

AB = ${\boxed{\sf{6.5}}}$

Step-by-step explanation:

Here's the required formula to find distance between points :

${\longrightarrow{\small{\sf{Distance = \sqrt{\Big(x_{2} - x_{1} \Big)^{2} + \Big(y_{2} - y_{1} \Big)^{2}}}}}}$

As per given question we have provided that :

• $x_2 = 6$
• $x_1 = 0$
• $y_2 = 3.5$
• $y_1 = 1$

Substituting all the given values in the formula to find the distance between points A(0, 1) and B(6, 3.5) :

${\implies{\small{\tt{AB = \sqrt{\Big(x_{2} - x_{1} \Big)^{2} + \Big(y_{2} - y_{1} \Big)^{2}}}}}}$

${\implies{\small{\tt{AB = \sqrt{\Big(6 - 0 \Big)^{2} + \Big(3.5 - 1\Big)^{2}}}}}}$

${\implies{\small{\tt{AB = \sqrt{\Big( \: 6 \: \Big)^{2} + \Big(2.5\Big)^{2}}}}}}$

${\implies{\small{\tt{AB = \sqrt{\Big( 6 \times 6 \Big)+ \Big(2.5 \times 2.5\Big)}}}}}$

${\implies{\small{\tt{AB = \sqrt{\Big(36\Big)+ \Big(6.25\Big)}}}}}$

${\implies{\small{\tt{AB = \sqrt{\big(36 + 6.25\big)}}}}}$

${\implies{\small{\tt{AB = \sqrt{42.25}}}}}$

${\implies{\small{\tt{AB =6.5}}}}$

Hence, the distance between points AB is 6.5

$\rule{300}{2.5}$

Answer 2

Answer:

AB = 6.5

Step-by-step explanation:

If you use the distance formula, you can find the answer.

$\begin{array}{l}AB=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\=\sqrt{\left(6-0\right)^2+\left(3.5-1\right)^2}\\=\sqrt{6^2+2.5^2}\\=\sqrt{36+6.25}\\=\sqrt{42.25}\\AB=6.5\end{array}$

Therefore, the distance between the points A(0, 1) and B(6, 3.5) is 6.5. Hope this helps!